In its first three years of operation, the Large Hadron Collider at CERN has already proved its worth as a discovery machine and reinvigorated the prospects for discovering new dynamics beyond the Standard Model. This thesis presents a range of experimental methods devised for discovery of supersymmetry, one of the most important extensions of the Standard Model being tested at the LHC. The first chapter discusses the concepts behind a set of transverse mass-bound variables, and explores connections between these variables and others in the literature. Not only are these variables important tools for mass measurement, should sparticles be seen at the LHC, they are also critical components of experimental searches. Accordingly, their performance has been compared in both mass measurement and search contexts, and the results are reported here. This is followed by the details of a search for hadronically-decaying squarks and gluinos, carried out on 4.7 fb−1 of data collected at 7 TeV in 2011 by the ATLAS detector. The search strategy is described, focusing on the implementation of a background estimation method using photon events to determine the background contamination due to invisible Z boson decays. The results of the search are then presented. Stringent limits are set on the production of squarks and gluinos in a variety of model scenarios.